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Beliebt Rechnen >

integral from 0 to 5 of (x-3)/(x^2-5x-6)

Lösung

\int_{0}^{5} \frac{x - 3}{x ^{2} - 5 x - 6} d x

Lösung

\frac{1}{7} ln (6)

+1

Dezimale

0.25596 \dots

Schritte zur Lösung

\int_{0}^{5} \frac{x - 3}{x ^{2} - 5 x - 6} d x

Ermittle den Partialbruch von

\frac{x - 3}{x ^{2} - 5 x - 6} : \frac{4}{7 ( x + 1 )} + \frac{3}{7 ( x - 6 )}

= \int_{0}^{5} \frac{4}{7 ( x + 1 )} + \frac{3}{7 ( x - 6 )} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{5} \frac{4}{7 ( x + 1 )} d x + \int_{0}^{5} \frac{3}{7 ( x - 6 )} d x

\int_{0}^{5} \frac{4}{7 ( x + 1 )} d x = \frac{4}{7} ln (6)

\int_{0}^{5} \frac{3}{7 ( x - 6 )} d x = - \frac{3}{7} ln (6)

= \frac{4}{7} ln (6) - \frac{3}{7} ln (6)

Vereinfache

\frac{4}{7} ln (6) - \frac{3}{7} ln (6) : \frac{1}{7} ln (6)

= \frac{1}{7} ln (6)

Graph

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